Table 3. Differences of Mean Error Scores from Zero

Dependent measure: (estimated distance - actual distance)

Pretest mean: -19,30 sd: 46.43  n: 240 _ tstatistic: -6.44
\ Posttest mean: 0.01 sd: 29.94 on: 240  tstatistic: 0.00

p<0.001

nonsignificant J

~

(-sependent measure: (estimated distance - actual distance)

—TM

Egocentric mean: -22.91 s.d: 39.75  n: 192 _ tstatistic:_-7.98 p< 0.001
\Exocentric mean: -0.80 sd: 38.09 on: 288  tstatistic: -0.35 nonsignificant |)
dependent measure: Ln ( estimated distance / actual distance )

Pretest mean: 0,33 sd: 0.45 n: 240 tstatistic: -11.48 p< 0.001
\ Posttest mean: -0.01 sd: 0.29 on: 240 _ tstatistic: -0.84 nonsignificant |)

Dependent measure: Ln ( estimated distance / actual distance )

Egocentric mean: -0.31 — s.d:0.39 n: 192  t statisti : p< 0.001
\Exocentric mean: -0.08  s.d.:0.40 n: 288 _tstatistic: -3.50 p< 0.001 yr,

14



consistent: 12+20>10
inconsistent: 12+ 20<10

225
200 ° ° ° ° ° ° ° °
175 ° ° °
150 4 ° ° °
125 ° ° °
100 4 ° ° °
75 ° ° °
50 ° ° °
25 ° ° °
oF 0 Position of observer
25
° 25 50 7 100 125-150, 178200225

Figure 4. Triangles Among Targets in a Field

The positions of three targets (or two targets and the position of the observer) define a triangle on the ground.
Judgments on the sides of this triangle can be compared for their consistency, in terms of the triangle inequality.
The three judgments (that represent the three sides of the triangle) are inconsistent if the two shorter estimates of the
three estimates do not sum to more than the third estimate. Four targets and the observer’s position define ten
triangles on the ground. We can count the number of times that triads of judgments violate the assumption that the
sum of two shorter distances are greater than the longer distance, among judgments of distance on those triangles.
This count (between zero and ten) is taken to indicate the geometric consistency of an observer’s judgments on a
trial.

RESULTS

The results of the experiment can be stated simply: Training improves performance
under NVG viewing conditions, and that improvement persists for at least one week. Observers
learn to estimate distances quickly with NVG devices under the illumination conditions of the
experiment. Though their verbal estimates of distance have an initial bias of underestimation, and
though their estimates have small but persistent differences, observers soon lear to estimate
distance accurately when given direct feedback. As a reflection of that accuracy, the geometric
consistency of observers’ estimates also increases with feedback. These improvements in
consistency and accuracy transfer to unguided performance, both immediately after training, and



60

2-0 Pe
Pong
eo
8 20 4 oat
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3 ie,
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53 “ a", © Observer six
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58 vas . TM © Observer nine
BE go 8 he © Observer twelve
53 deg RD Sepa
35 71 gM
22 . ost,
33 -
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2 .
EE wis
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60
20 40 60 80 100

Number of judgments

Figure 7. Concluded

A moving average of the error scores can be computed. A 21-point moving average is computed as follows: The first
21 judgments are averaged--essentially the entire first trial. Then the first judgment is dropped, the 22nd judgment
added, and a new mean calculated. Then the second judgment is dropped, the 23rd judgment added, and another new
mean calculated, and so on. The moving average is used to indicate trends in time series. A 21-point moving average
is plotted for the second through fourth trials of the experiment (the first training: judgments 21 to 40; second training:
Judgments 41 to 60; first posttest: judgments 61 to 80; and second posttest: judgments 81 to 100) by number of
judgments made by each observer. The moving average is computed on the signed error score of estimated distance
minus actual distance. Individual results are plotted; not all observers took part in all the posttest conditions.
Judgments become accurate with feedback training; the judgments of some individuals do depart from precise
performance in the posttest conditions.

18



Table
No.

FIGURES

Page

Mean Error in Distance Estimates: Reising & Martin (1995)..ccsssssssssssssssssssssssssee 3
Variability of Error in Distance Estimation: Reising & Martin (1995) .............0... 4
Targets in an Open Field ........ssssssssssssssssseeessessssssstsssssssssssssssessssrsssssseseessaseesees 6
Triangles among Targets in a Field. 8
Effect of Feedback on Distance Estimates 11
Effect of Feedback on Consistency of Judgments......ccccscccssssssssssssssesesssecceseeseseseees 16
Moving Averages of Difference Scores for Individual Observers.......scssssssssssssssse 17, 18
Moving Averages of Ratios for Individual Observers ......ccccsssssesssssssssesssssssecsssseseee 19, 20
Distance versus Angular Subtense.......s.ccccsssssssssccsssssesssssssssssessseersvecsessssssnsccesssseces 24

TABLES

Accuracy over Trials, as Assessed by Three Dependent Measures ......ccccccssssseeeoes 10
Summary Table for Analysis of Variance .........ccccssscscssssssssssssssssssssssessssssssssssssssees 12
Differences of Mean Error Scores from Zero... 14
Individual Differences of Mean Error Scores.....ssssssssssssssssstsssssssssssesssssssssssssssesesee 15
Consistency of Distance Judgments, in Terms of Triangle Inequalities................. 15
Summary of Regression Analyses ..........ssssssssssssssssssssssssssesssssssssisssssssstessnnasnsnasess 22
23



Table 4. Individual Differences of Mean Error Scores

The effect of feedback on distance estimates varies from observer to observer. Here mean differences in estimate are
tabled for the pretest condition (before feedback), for immediate testing after feedback, and for testing a week after
feedback. One tabled score is the mean of twenty scores, each the difference between an estimated distance and an
actual distance. Most observers improve markedly in performance.

Observer Pretest Immediate One week

1 -50.6 * -4.2

2 -58.1 -13.2 *

3 -19.4 30.9 33.6

4 42.3 * 27.0

5 -23.4 23 *

6 11.7 -0.4 -3.7

7 -6.7 * 5.5

8 45.3 19.8 *

9 -18.3 -24.3 -28.1
10 48.4 * 7.9
11 32.7 -0.3 *
12 -48.0 -23.9 -26.2

Table 5. Consistency of Distance Judgments in Terms of Triangle Inequalities

A measure of consistency of distance judgments is tabled for trials of the experiments. Observers made 20 judgments
of distance on each trial (i.e., two sets of ten judgments). The distances formed connected figures, so an observer might
judge the distance between points 1 and 2, later the distance between points 2 and 3, and that between points 3 and 1.
Triads of judgments on the sides of a triangle like this will obey the triangle inequality, if those judgments are
consistent. If the first distance between points | and 2 is the longer side of this triangle, then the observer’s three
judgments of sides 12, 23, and 31 are consistent if the estimated length of 12 is less than the sum of the estimated
lengths of 23 and 31. (The labels may be permuted, should the subject judge side 23 to be the longer side of the
triangle.) If the three distances are consistent, then a tally is added to the count of the consistency measure.

Consistency Measure (based on number of violations of the triangle inequality)

Trial Count Proportion Total n
1 24 55 133 240
2 23 69 159 230
3 24 79 190 240
4 16 77 124 160
5 16 -76 122 160
15



The experiment that has been reported includes a number of conditions including:
standing observation, elevated observation, distances that are radial from the observer (egocentric
distances), distances that are not radial from the observer (exocentric distances), and the three
test conditions (pretest, trial 1; feedback, trials 2 and 3; and posttest, trials 4 and 5). For each of
the combinations of these conditions, the relation of estimates of distance may be compared to
both actual distance and visual angle. For the sake of brevity and clarity, instead of visual angle
we use the tangent of visual angle in the present examples. (Boff, Kaufman, & Thomas, 1986,
use cotangent from the visual horizon rather than the tangent of visual angle, but this is a
superficial difference. Also, similar results are obtained with the raw measure of visual angle.)

Regression analyses (simple linear regressions) were performed for each of the conditions
of the experiment, both for actual distance versus estimate of distance, and tangent of visual
angle versus estimate of distance. Regression scatterplots can be drawn for 12 conditions: the
combinations of two conditions or types of distances (egocentric, exocentric), two viewing
heights (standing or elevated), and three test conditions (pretest, feedback, posttest). We may ask
two simple yes-or-no questions of these results: (1) Is the slope of each regression line different
from zero? i.e. if the regression coefficient is significant at a level of x = .05; and (2) If it is
significant, we may ask if the statistical estimate of the regression coefficient could include one,
ie. if the confidence interval of the estimate of slope includes one. A regression coefficient of
one indicates a perfect correspondence between the variables.

A simple pattern emerges from this mass of results (Table 6). All scatterplots that relate
estimated distance to actual distance had a slope significantly different from zero. All of those
scatterplots had another property: The estimate of slope was not significantly different from one.
In conditions that involved exocentric distances, none of the scatterplots that relate estimated
distance to the tangent of visual angle had a slope significantly different from zero. In conditions
that involved egocentric conditions, all of the scatterplots that relate estimated distance to the
tangent of visual angle had a slope significantly different from zero. In those conditions, all of
the estimates of slope of the regression line were significantly different from one as well. In
other words estimated distance could (possibly) be predicted perfectly by actual distance for both
egocentric and exocentric distances. At the same time, estimated distance could not be predicted
perfectly by the tangent of visual angle, which does not produce any significant prediction of
estimated distance in the case of exocentric distances.

There is another way to consider the results, that leads to a similar conclusion. We have
three variables, one dependent (estimated distance) and two independent (actual distance, visual
angle). We can consider four conditions: direct feedback trials for egocentric distances (trials 2
and 3), direct feedback trials for exocentric distances (trials 2 and 3), posttest trials for egocentric
distances (trials 4 and 5), and posttest trials for exocentric distances (trials 4 and 5). In each of
these conditions, we can ask what the relation of two variables may be, discounting the effect of
the third. We do this because the tangent of visual angle is correlated with actual distance in the
experiment. (The relation between egocentric distance, exocentric distance, and visual angle is
diagrammed in Figure 9 for the conditions of the present experiment.) We want to determine:

21



60

© Observer one

© Observer four

5 Observer seven

= Observer ten

Moving average (21 point)
estimated distance minus actual distance

20 40 60 80 100

Number of judgments

60

Observer two
Observer five
Observer eight

eoeo

Observer eleven

Moving average (21 point)
estimated distance minus actual distance

60

20 40 60 80 100
Number of judgments

Figure 7. Moving Averages of Difference Scores for Individual Observers

17



Table 2. Summary Table for Analysis of Variance

Dependent measure: In (estimated distance) - In (actual distance)

Source df SS F statistic

Test (pretest/posttest) 1 11.90 10.21 p<.0l
Test X Subjects 11 12.82

Position (ground/elevated) 1 0.09 0.92 “nonsignificant
Position X Subjects 11 1.13

Test X Position 1 0.08 1.15 nonsignificant
Test X Position X Subjects 11 0.80

Distance Type 1 5.96 55.35 p<.0l
(egocentric/exocentric)

Distance Type X Subjects 11 1.18

Test X Distance Type 1 0.03 0.67 nonsignificant
Test X Distance Type 11 0.63

X Subjects

Position X Distance Type 1 0.01 0.12 nonsignificant
Position X Distance Type 11 0.98

X Subjects

Test X Position 1 0.03 0.56 nonsignificant
X Distance Type

Test X Position 11 0.65

X Distance Type X Subjects

12



—O— Treatment group
—O— Control group

30

=
=
5
g —
2 2» —2
4
Hy
&
&
3
2 10
3s
:
Es
a

o

° Pretest Posttest -

Test time

40
20 oO

=
£
5
3
2 20
Ey
3 NSN
§ —*— Treatment group
a —O— Control group
3
z 10
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a

0

> Pre-test Post-test aa

Test time

Figure 2. Variability of Error in Distance Estimation: Reising & Martin (1995)

Variability of error in distance estimates is plotted for conditions of Reising and Martin’s (1995) experiment. The
upper graph plots the standard deviation in absolute values of the difference between estimated distance and ground
distance. The lower graph plots the standard deviation in values of the difference between estimated distance and
ground distance, but preserves the sign of the difference. These values are graphed by condition of test (pretest,
posttest) and group (treatment or control).



REFERENCES

Antonio, J. C., & Berkley, W. E. (1993). Night vision goggle model F4949 preflight adjustment/
assessment procedures. (AL/HR-TR-1993-0111, AD A271 079). Mesa, AZ: Armstrong
Laboratory, Human Resources Directorate, Aircrew Training Research Division.

Boff, K. R., Kaufman, L., & Thomas, J. P. (1986). Handbook of perception and visual performance.
2 vols. New York: John Wiley and Sons.

Bourdy, C., Cottin, F., & Monot, A. (1991). Errors in distance appreciation and binocular night
vision. Ophthal. Physiol. Optics, 11, 340-349.

Crowley, J. S. (1990). Human factors of night vision goggle (NVG) helicopter accidents [abstract].

Aviation, Space, and Environmental Medicine, 61, 508.

DeLucia, P. R., & Task, H. L. (1995). Depth and collision judgment using night vision goggles.
International Journal of Aviation Psychology, 5(4), 371-386.

Ferris, S. H. (1972). Improvement of absolute distance estimation underwater. Perceptual and
Motor Skills, 35, 299-305.

Ferris, S. H. (1973). Improving absolute distance estimation in clear and in turbid water.
Perceptual and Motor Skills, 36, 771-776.

Foyle, D. C., & Kaiser, M. K. (1991). Pilot distance estimation with unaided vision, night-vision
goggles and infrared imagery. Society for Information Display International Symposium
Digest of Technical Papers, 22, 314-317.

Gibson, E. J., & Bergman, R. (1954). The effect of training on absolute estimation of distance over
the ground. Journal of Experimental Psychology, 48(6), 473-482.

Gibson, E. J., Bergman, R., & Purdy, J. (1955). The effect of prior training with a scale of distance
on absolute and relative judgments of distance over ground. Journal of Experimental
Psychology, 50(2), 97-105.

Higashiyama, A. (1996). Horizontal and vertical distance perception: the discorded-orientation
theory. Perception and Psychophysics, 58(2), 259-270.

Higashiyama, A., & Shimono, K. (1994). How accurate is size and distance perception for very far
terrestrial objects?: Function and causality. Perception & Psychophysics, 55(4), 429-442.

Levin, C. A., & Haber, R. N. (1993). Visual angle as a determinant of perceived interobject
distance. Perception & Psychophysics, 54(2), 250-259.

27



part of the optical conditions of stimulation whose influence can be ameliorated by training. For
the purposes of the estimation of distance, at the elevation angles we have studied, estimates of
these distances are still best predicted by their associated distances. (One might consider,
though, that an elevation of the observers over a full range, from standing position to bird’s-eye
view, might have had some effect on estimates of distance. The more elevated the eye point of
the observer from the ground plane, the less will be the effect of foreshortening upon distances in
the ground plane.)

180
150 4 :
8 °
» 2
3 ° 3
5 °
2 Be %% 29 8
3 20 ened 28 g mee @ 3303 3 0 Gp 808
z -° of & 98,2 06
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of o Be @o &y
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a) °
8 a oo B 3
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o 50 100 150 200
ey jc!
Distance ‘Egocentric' lengths

© ‘Exocentric' lengths

Figure 9. Distance versus Angular Subtense

“Egocentric” distances are different from “exocentric” distances in the experiment: They are different in their geometry.
The distances used in the experiment are plotted against the visual angle subtended by those distances. “Egocentric”
lengths appear as solid dots, while “exocentric” distances appear as unfilled dots. While exocentric distances span a
range of angles, egocentric distances fall close to 90° of visual angle. Egocentric distances are maximally
foreshortened in contrast to other distances. The dots that indicate egocentric distances appear to form two curved
lines; the two lines correspond to the standing and elevated conditions of observation used in the experiment.

DISCUSSION

Observers estimated distance well on average in the present study. Yet in discussion on the
psychology of vision, many reasons are offered why observers should not discern distances with
accuracy. The greater number of those reasons involves consideration of foreshortening. The story
of foreshortening begins as follows: Distances in a landscape are not generally preserved in a
photograph of the landscape. That is, photogrammetry and mapping do not proceed by measuring

24



DISTANCE ESTIMATION WITH NIGHT VISION GOGGLES:
A DIRECT FEEDBACK TRAINING METHOD

INTRODUCTION

Night vision goggles (NVGs) are used in both rotary-wing and fixed-wing aircraft to
enhance the ability to conduct operations under cover of darkness. NVGs provide an intensified
image of landscapes illuminated by ambient energy in the night environment; specifically, the
photosensitive components of the goggles are most sensitive to the red and near-infrared portion of
the electromagnetic spectrum (approx. 600-900 nanometers). The NVG device amplifies the
energy in this portion of the spectrum: Luminance of the post-objective image can be between
2,000 to 7,000 times that of an image that enters the goggles. As a consequence of their design,
most NVGs affect field of view (FOV) and resolution as well. Depending on their make and type,
they provide a limited FOV of approximately 40 deg of visual angle; visual acuity can be expected
to be approximately 20/30 Snellen acuity at best, under optimal lighting conditions.

Since NVGs have a restricted field of view and a diminished resolving power when
compared to the capability of the unaided human eye in daylight, we can anticipate that NVG users
unaccustomed to these altered viewing conditions may experience misperceptions or illusions.
Numerous field reports suggest that NVG viewing does induce misperceptions that compromise
flight safety, including difficulty in judging ground distances or the separation of objects. Foyle
and Kaiser (1991) reported that NVG-aided distance estimation is significantly poorer than unaided
distance estimation on the ground in daylight. Crowley (1990) tasked helicopter pilots to maintain
a set altitude under NVG or unaided daylight conditions. Pilots made significantly more errors in
the former than in the latter condition. The misperception of distance with NVGs was attributed to
limits on resolution rather than to limits on the field of view. By contrast, DeLucia and Task (1995,
p. 383) find “effects of NVGs (compared to unaided vision) did not occur in the field when
participants judged when to initiate a turn to maneuver a car in front of a wall without collision.” In
addition, there may be important differences between judgments with NVGs made on the ground
and those made in the air.

The present experiment is one of a series conducted under NVG conditions, to determine
how distance estimation can be improved with structured training. The earlier studies are reported
by Reising and Martin (1994, 1995); they employed a training procedure known as “perceptual
calibration.” Observers saw targets at distances known to them (i.e., “this is what a hundred feet
looks like on the ground”), and the observers were instructed to “calibrate their eyes” to those
distances. The procedure has some affinity to the way pilots report they learn to gauge altitude by
sight. Pilots will view the out-the-window scene, then check a distance-rendering instrument--such
as a radar altimeter--to put a number to the aircraft’s altitude. They will then view the target from
another distance and check the instrument again. It is this cycle of observation and instrument
reading that has become known as perceptual calibration.

In Reising and Martin’s experiments, observers were able to read distance markers placed
next to targets. These markers indicated the distance between the target and the observer’s position
(the egocentric distance of the target). The observers were also informed of the unmarked distances



PREFACE

This report documents the effectiveness of direct and immediate feedback at reducing errors in
estimation of distance under night vision goggle (NVG) conditions. NVG-aided distance estimation
was assessed at a standing position and at an elevated position (to an eye height of about 12 ft).
Training was administered on the ground for some subjects and at an elevated position for other
subjects. Retention of this feedback training was assessed by NVG-aided distance estimation after one
week. Direct feedback is effective in reducing errors in distance estimation. Improvements in
performance persisted for at least one week after training.

The work was conducted by the Armstrong Laboratory, Aircrew Training Research Division
(AL/HRA), under Work Units 1123-B4-06, Night Vision Device Training Research, and 1123-B2-06,
Aircrew Training Research Support. Support was provided by Hughes Training, Inc. (HTT), Training
Operations, under contract F41624-95-C-5011. HTI supports AL/HRA by supplying night vision
device subject matter expertise and human factors expertise in the areas of research, development, test,
training, and evaluation. We would like to acknowledge Peter Froeb’s patient assistance in conducting
the experiment reported here.



when the difference between the estimated and actual distances approaches zero (when their log
ratio approaches one). Do the difference scores in these conditions depart from zero (rather than
simply being different one from another)? Table 3 makes these comparisons explicit. While
pretest scores are different from zero in terms of the signed difference of distances, posttest
scores are not significantly different from zero. Error scores for egocentric distances are also
farther from zero than are error scores for exocentric distances overall.

Individual differences do persist: In terms of the difference between estimated distance
and actual distance, there was either consistent overestimation or underestimation of distances by
several observers. That is, observers differ in their ability to judge distance, despite training.
Reising and Martin (1995) found that “subjects still vary as much as 6 ft on the critical distances
(40 - 60 ft) after training.” With regard to the present experiment, individual differences between
mean pretest scores and mean posttest scores are listed in Table 4. The source of these individual
differences has not been explored; such differences have been attributed to differences of lens
accommodation and convergence of the eyes (e.g., Bourdy, Cottin, and Monot, 1991), but that
kind of speculation goes well beyond the evidence of the experiment.

Observers became more consistent in their judgments of distance as they became more
accurate. Each trial consisted of many judgments of distance. Some of these distances were
connected in triangles (compare Fig. 4). Two groups of ten triangles could be formed from the
distances presented in each of the five trials. For each of these triangles, it can be asked if the
observers’ judgments were consistent. The three judgments (that represent the three sides of the
triangle) are inconsistent if the two shorter estimates do not sum to more than the third estimate.
The number of times that the two shorter estimates do sum to more than the third can be taken as
a measure of consistency of the observers’ judgments. (The measure is tallied in Table 5.) In the
experiment, distances among four targets and the distances of those targets to the observer define
ten distances. Because all the targets are joined by distances, the four targets also define ten
triangles. If the targets are {1,2,3,4} and the observer’s position is {0}, then the triads of
distances define ten triangles: {1,2,3; 1,2,4; 1,2,0; 13,4; 1,3,0; 1,4,0; 2,3,4; 2,3,0; 2,4,0; 3,4,0}.
During the pretest the observers’ estimates were not consistent (only 55% of triads qualified), but
their consistency improved with feedback (to 79% of triads, Fig. 6). Computation of this
measure is a way of tallying the geometric consistency of responses; the existence of changes in
the measure does not imply that observers used any particular method to improve the consistency
of their judgments, such as learning to triangulate distances.

Time-series plots can be made of the data to illustrate the training effect of immediate
feedback for each observer. Each observer makes 20 judgments of distance on each trial. A 21-
point moving average was taken across all estimates for each observer, and these are displayed in
Figures 7 and 8. Performance becomes accurate with feedback and drifts from accuracy with
time, though the performance of most observers is better on average at the end of the experiment
than in the beginning.

13



30
Ow
25
(20
g
£ 8
3 TM~
3
£
# 10
s —Se— Training group
=
—e— Control group
5
°
o Pretest Post-test Ld
Test time
10
—_—®—= Training group
—O—— Control group
5
° —s
z —
g 5
5
2
2
5
2 40
2 oo”
45
-20
co Pre-test Post-test iad

Test time

Figure 1. Mean Error in Distance Estimates: Reising & Martin (1995)

Mean error in distance estimates is plotted for Reising and Martin’s (1995) experiment. The upper graph plots mean absolute values
of the difference between estimated distance and ground distance. The lower graph plots mean values of the difference between
estimated distance and ground distance, but preserves the sign of the difference. These values are graphed by condition of test
(pretest, posttest) and group (treatment or control). When the sign of errors in estimate is taken into account, the interpretation of
mean differences in the experiment is altered. The mean absolute values are: (treatment pretest: 26.5 ft), (treatment posttest: 13.4
ft), (control pretest: 26.2 ft), (control, posttest: 24.3 ft). The mean signed values are: (treatment pretest: -2.4 fi), (treatment posttest:
-0.3 ft), (contro! pretest: -13.3 ft), (control, posttest: -9.8 ft).



=
a3
Be
Se
g2
ag
2 il
32
=e
&
044
02
20 40 60 80 100
Number of judgments
18
164
144

8
zs
32
as
3
£8
se
ae
5
Ps
$2
33
£

02
ot 20 40 60 80 100

Number of judgments

eoeo

Observer one
Observer four
Observer seven

Observer ten

Observer two
Observer five
Observer eight

Observer eleven

|
|
Figure 8. Moving Averages of Ratios for Individual Observers
19



UNITED STATES AIR FORCE
ARMSTRONG LABORATORY

DISTANCE ESTIMATION
WITH NIGHT VISION GOGGLES:
A DIRECT FEEDBACK TRAINING METHOD

Keith K. Niall

US/Canada Scientist and Engineer
Exchange Program Participant

Jack D. Reising
HUGHES TRAINING, INC, Training Operations

6001 South Power Road, Bidg 561
Mesa AZ 85206-0904

Elizabeth L. Martin
Marcus H. Gregory, 1Lt, USAF
HUMAN RESOURCES DIRECTORATE
AIRCREW TRAINING RESEARCH DIVISION

6001 South Power Road, Bldg 558
Mesa AZ 85206-0904

June 1997

DTIC QUALITY INSPECTED 2

997008 124

AIR FORCE MATERIEL COMMAND
Armstrong Laboratory

Approved for public release; distribution is unlimited. Human Resources Directorate

7909 Lindbergh Drive

Brooks Air Force Base TX 78235-5352



200

175

150

125

foot

0 2% 80 75 100 125 150 175 200 225

feet

Figure 3. Targets in an Open Field

The experiment was conducted in an open field. Targets could be positioned in one of 64 locations; though eight
targets were present in the field at once, only four of these were used at one time. The positions of the four targets (1, 2,
3, and 4) plus the position of the observer (marked 0) define ten distances among locations. Observers were asked to
estimate each of these distances. The arrangement of the targets was determined in advance by random assortment. A
less schematic overview is included as well, to clarify the relation of the observer to the ground plane.



only intermittent recurrent training. This experiment assesses whether distance estimation
performance can be improved, and whether improvement persists for at least one week after
training. Observers in the experiment view a number of distances both from standing and from
elevated vantage points. This is done in order for the experimental analysis to distinguish between
the effects of visual angle and distance on judgments of distance.

METHOD
Observers

Twelve observers (9 male and 3 female) volunteered for the experiment. All observers had
at least 20/20 photopic visual acuity and received specific training on F4949 NVG adjustment
procedures (as described by Antonio & Berkley, 1993). Ages ranged from 21 to 40 years, with a
mean of 33.6 years. None of the observers had previous experience with NVGs. All demonstrated
at least 20/30 NVG-aided visual acuity after NVG adjustment as measured with a Hoffman
Engineering ANV-20/20 NVD Infinity Focus System.

Apparatus and Stimuli

The experiment was conducted in a large open field. A few trees were visible about 300 yd
beyond the test area. Some cultural lights were visible in the far distance; none were located within
3 mi of the direction of gaze of the test area, and most were more than 15 mi away. The area was
divided into a 175 x 175 ft square grid, marked off in 25 ft increments. The markings that defined
these increments were not visible through NVGs, but they were retained for the purpose of
arranging the stimuli. At any one time, eight targets were randomly positioned in 8 of 64 distinct
locations defined by the 25 ft increments of the grid (Fig. 3a). The targets consisted of white
cylinders that were approximately 2 ft high and 1 ft in diameter. Each cylinder was raised on a pole
approximately 2 ft high. Observers viewed the targets 25 ft away from the midpoint of one edge of
the square. Observers viewed the targets both from the ground and elevated on a platform that
could be reached by stairs. (See Fig. 3b. The platform was a standard B-1 stand used for aircraft
maintenance.) The stand raised the observers 7 ft 7 in. loff the ground, from the base of the wheels
to the floor of the platform. All testing was conducted under clear starlight conditions, though the
presence of cultural lights increased ambient illumination. NVIS radiance (as defined in Military
Specification, MIL-L-85762A. Lighting, Aircraft, Interior. Night Vision Imaging System (NVIS)
Compatible), measured from the targets was 3.62 x 10° NR,, which is approximately equivalent
to a quarter moon. The radiance was measured with a Hoffman Engineering NVG-103
Inspection Scope. The NVG used was a Class A ITT F4949D (S/N 2590).



viewing conditions (given the limits of the experiment in terms of range of distances, and other
factors).

CONCLUSION

Observers improved their ability to estimate distance and this improvement persisted for
at least one week. It did not make a significant difference whether observers were tested at eye
level, or slightly elevated on a B-1 stand. Distances between the observer and an object were less
well estimated than distances between two objects, presumably because of the severe
foreshortening due to perspective on ground distances viewed from eye height or nearby. The
distances examined in this experiment have most relevance to the “close-in” judgments that are
made in helicopter operations.

Future Research

Providing immediate verbal feedback does produce accurate performance in the long run.
There are many issues that remain to be addressed. A planned experiment will touch upon issues
(a) of time restrictions, (b) of criterion-referenced training (that is, training to a stable level of
proficiency), and (c) of transfer of training from unaided daylight conditions to estimates made
under NVG conditions. In this prospective experiment, observers will be trained to criterion; they
will be trained until they achieve a certain tolerance in terms of relative distance, i.e., until their
performance in terms of the ratio of the distance they estimate to the actual distance is close to 1.0,
for a number of estimates in a row. Though the testing will be done at night under conditions of
NVG viewing as before, the training with immediate feedback that will be given before the testing
will be either under daylight conditions or under NVG viewing conditions. It may be that a certain
amount of training in daylight can substitute for a large amount of training under conditions of
NVG viewing. The testing procedure in this experiment will have an additional constraint:
Observers will be required to give their answers within a short interval of time. Responses that do
not fall within the required interval (a variable interval measured in seconds) will be recorded by
the experimenter, but counted as successful responses only if given in the time allotted. This
condition parallels the many operational conditions in which relatively rapid judgments must be
made.

26



lengths in pictures taken from eye height. Instead, strict methods are applied in aerial photography
to obtain pictures from a vantage directly above a portion of the landscape to be mapped. Pictures
taken from oblique angles are susceptible to foreshortening, which is a general name for the
compression of distances due to perspective in a picture. The effect of foreshortening can be
described simply when, as in our experiment, the distances to be compared lie on a flat surface or
ground plane.

The nature of foreshortening provides a clue to what has been thought to be a psychological
difference between the judgment of egocentric distance and that of exocentric distance. The
judgment of distance has been thought to depend on the apprehension of visual angle (or as the
tangent of visual angle); we have seen in this experiment that the evidence runs contrary to that
assumption. Under foreshortening, distances are shortened more in projection as the angle they
make to the picture plane increases. That is, the picture image of a distance nearly end-on is
severely shortened, and the picture image of the same distance taken broadside is less shortened.
The relation can be expressed more exactly: The shortening of the distance varies according to the
cosine of the angle that that distance makes with the picture plane. Now the rate of change of the
cosine function is not great between 0° and 15°. The rate of change of the function is greater
between 80° and 85°.

Contrast this with the tangent function of visual angle. The tangent function, or visual angle
itself, has been considered important because psychologists have claimed that observers apprehend
visual angle and, from there, they deduce or infer or interpret information about distances on that
basis. That is an unnecessary assumption, a theoretical confusion that may have no foundation in
fact. What may have encouraged psychologists in this matter is that sometimes foreshortening has
an effect on the estimation of distance. Foreshortening varies as the cosine of the slant of a line
length to the picture plane. Line lengths that are most severely foreshortened are not judged so
well; hence, “egocentric” distances are badly judged in contrast to “exocentric” distances in
general. But the distinction has little to do with any special status of egocentric distances in
psychological terms. Rather, egocentric distances are special in geometric or optical terms, because
they represent line lengths that lie closest to being “end-wise to the eye.” This difference is not
changed by training. (Nor was there a significant interaction of Distance Type and Test in the
ANOVA that was reported.)

If the optical conditions are changed under which distances are judged, then performance
may change as a consequence. Performance may not transfer adequately from one set of optical
conditions to another, but this is not in itself a psychological matter (see Ferris, 1972; 1973). Many
psychological effects on the untrained estimation of distance have been claimed. Higashiyama
(1996) claims that distance estimation changes when observers are standing, lying on their sides, or
lying on their bellies. Yet such differences may be malleable performance effects rather than a
teflection of the observers’ competence. In the study of competence, we catch subjects at their best.
In the evaluation of distance, “best” simply means accurate performance. Whatever other
objections there may be in psychology to the accurate estimation of distance by eye, the results of
the experiment are that such estimates are accurate (precise in the sense of being dead-on in
average) when observers are given simple feedback on their performance, even under NVG

25



between a pair of targets (called exocentric distance). Reising and Martin (1995) concluded that
absolute error in distance estimation was significantly lower on average for a group that had
undergone “perceptual calibration” than for a control group. A review of the data revealed no
significant improvement in NVG-aided distance estimation when signed error was the dependent
variable of the analysis, rather than absolute error in distance (See Fig. 1).

Using signed error in distance as the dependent measure, there was a significant and
substantive difference between groups in the pretest condition. The treatment group had an initial
advantage. The mean magnitude of this difference between groups was unchanged at posttest,
though both groups’ estimates improved slightly. Then the two groups appeared as different in
amount of improvement, because the variability of errors in the treatment group was reduced
between pretest and posttest (Fig. 2). The change in variability is just as well represented by
inspection of the variability of the signed errors. When absolute errors are computed, there is an
interaction between test means and group means. That interaction was interpreted as an
improvement in mean performance for the treatment group over the control group. The interaction
is the result of a difference in the variability of error scores, which can be noticed in the variability
of the signed scores. The use of absolute values confounds mean tendency and changes in
variability. The appearance of an interaction in mean tendency for the absolute scores is an artifact
due to the copresence of two factors: (a) a pre-existing difference between treatment and control
groups, and (b) the posttest scores of the treatment group centered about zero. The use of signed
error may be termed a wider interpretation in the choice of a dependent measure and the use of
absolute error may be termed a narrower interpretation, in the sense that signed error includes
information that is omitted in absolute error. The narrower interpretation forestalls one possible
conclusion from a set of results: It prevents the conclusion that there is accurate performance in the
presence of variation about the mean. Questions persist of the best dependent measure, and of the
efficacy of perceptual calibration techniques in improving distance estimates. These questions are
not specific to the study at hand. For example, root mean square (RMS) measures are commonly
applied to gauge deviation from flight paths. (As for the dependent measure, it may be that some
other measure--such as the ratio of estimated distance to ground distance--is better than the
difference of estimated distance and ground distance.)

The present experiment was conducted to determine the efficacy of a slightly different kind
of training for NVG-aided distance estimation, one of the most effective feedback techniques in
general: immediate and direct feedback. This has been shown to be an effective technique in
outdoor viewing without the use of NVGs, as in Gibson and Bergman (1954), and Gibson,
Bergman, and Purdy (1955). Direct feedback training occurs when observers are required to make
an explicit estimate of distance, and they are informed of the true ground distance immediately after
making their judgment.

Many issues relevant to training have not been addressed, including effects specific to
illumination levels and transfer of training, say from ground training to distance estimates made
from the air. It may be that pilots need to be trained before every mission to account for differences
in the perceived NVG scene that vary with operational conditions. Or, NVG-aided distance
estimation training may need to occur only under low illumination conditions and may transfer to
high illumination conditions. Furthermore, training may persist for an extended duration, requiring



250 5 L1 Remainder

BZ count

200 4

1504

100 4

Number of consistent triangles

2
s
3
3
Es

pretest K

Immediate
posttest

Figure 6
Effect of feedback on consistency of judgments

The number of consistent triangles implicit in observers’ judgments is tallied by trial in the experiment. Consistency in
judgment increases with training (direct feedback). ‘The proportion of consistent judgments remains high in both posttest
conditions after training. (There are fewer total judgments made in the posttest conditions, so the absolute count is lower.)
‘The proportions of consistent trials for different trials are: pretest 133/240, first training 159/230, second training 190/240,
immediate posttest 124/160, one week posttest 122/160. The number of total judgments is less by ten in the first training
trial, since one observer failed to make one judgment.

Those are the major results of the study. There are a number of other questions that arise
from theoretical concerns about judgments of distances. One account, perhaps the prevailing one,
is that observers cannot judge distance itself (for instance, as in Higashiyama & Shimono, 1994)
since distance is not “present to the eyes.” Instead, it is supposed that observers gauge the optical
angle subtended by a distance, and from the measure of that angle plus other information,
observers will unconsciously calculate distances, which then are reflected in the observers’
estimates (this explanation is recounted in Levin & Haber, 1993). A simpler account is that when
observers are asked to judge distance under NVG viewing conditions with or after feedback, they
do judge distance.

Reasons to question the former account emerge from the results of the present
experiment. One is that while estimated distances are well predicted by actual distances in every

16



Table 6. Summary of Regression Analyses

Independent var. Condition Height Trial Slope+0? Estimate includes 1.0 ?

actual ego low 1 v Vv
actual ego low 23 Vv v
actual ego low 45 v v
actual ego high 1 v v
actual ego high 2,3 v v
actual ego high 45 v v
actual exo low 1 v wo
actual exo low 23 v v
actual exo low 4,5 v Vv
actual exo high 1 v v
actual exo high 2,3 v Jv
actual exo high 4,5 v v
tan theta ego low v x
tan theta ego low 2,3 v x
tan theta ego low 4,5 v x
tan theta ego high v x
tan theta ego high 23 v x
tan theta ego high 45 v x
tan theta exo low 1 x

tan theta exo low 2,3 x

tan theta exo low 45 x

tan theta exo high 1 x

tan theta exo high 2,3 x

tan theta exo high 4,5 x

(a) if estimated distance is correlated with the tangent of visual angle, once the effect of actual
distance is held constant, and (b) if estimated distance is correlated with actual distance once the
effect of visual angle is held constant. This is accomplished by taking a partial correlation, as in
Table 7. Then a patter is clear: Estimated distance is strongly and significantly correlated with
actual distance when the effect of tangent of visual angle is held constant. Estimated distance is
not significantly correlated with the tangent of visual angle--anywhere--when the effect of actual
distance is held constant. The apparent effect of visual angle seems to be due to its dependence
on actual distance, and not vice versa. In conclusion it seems unlikely that judgments of distance
are formed by apprehending visual angles from which less reliable estimates of distance are
formed. More likely, observers estimate distance when asked to estimate distance.

22



CONTENTS
Page
INTRODUCTION ......scssssssssssetssssssecsssnscessssccsssssccssscsessnecesnsecessnsecessnseecanecessnascesaneeennseeseansesssy 1
METHOD ....sssssssssseccsssscssssccccsnsccessnsecsonseessnecssssusecssuecssssscssssessssssessssescessnecessssecessscesuneceesauecsens 5
ODSELVETS.....escssessccssessessseeccesssesssssesssssecssssuecsssssessseccssnscssssuecesssuccesnvecessuneessnccssunecesnneeesens 5
Apparatus and Stimulli........sscccsssssssscsssssssesseessnnneceesnnsseceecsonnnteseecnnneiesesssnneesssssnneeessss 5
Procedure see 7
Pretest. 7
Training. 7
Posttest 7
RESULTS cesssessssssssssssscssnsessssssecsssnvessssecssssssssssuesessusssssecsssnescssnsesessnecsssuecessasecsascessanecessnes 8
DISCUSSION . 27
CONCLUSION ..0...ssoesesssessessstessssseecsssssesssssessssecssssecesnessssuccsssssssssnessssssecssnecessanecsnnsecsnnecceaneess 28
Future Research ......ccsssesssessssssssssssssesssesssessssesssecssecssesensesssessnsssseessnccassessseacecaeecencenaes 28
REFERENCES ......scsccsssssssessessesessessesscenesecsesuescsnssncseenceneneenesscnesustesneenecussesnsnacsesasneensanensensanentes 29



after a delay of one week. Observers’ estimates of distance parallel actual distance, not visual
angle or its tangent function. There is a small (in terms of feet estimated) but robust effect that
may be attributed to the difference between “egocentric” and “exocentric” distance. Such effects
may best be explained by the influence of foreshortening rather than the product of some
psychological mechanism for the estimation of distance. The results of this experiment are
consonant with the view that foreshortening is not a cue for the estimation of distance; it is the
aggregate effect of perspective which impedes the estimation of distance.

Observers underestimated distances by 20 ft on average before training, while
performance did not differ significantly from perfect performance (in’ mean value, with some
variability) either during training or during posttests. Observers estimated distances accurately in
the first feedback trial. (“Estimate” will be used to designate a single response, while “trial” will
be used to designate a group of responses by an observer in one portion of the experiment. The
trials are counted as follows: 1. unguided pretest; 2. first feedback trial; 3. second feedback
trial; 4. immediate posttest; and 5. delayed posttest.) There are several ways to measure this
performance (Table 1). One is to take the signed difference of the verbal estimate from the actual
distance; another is to take the ratio of the verbal estimate to the actual distance. Both measures
follow the same pattern across trials (Fig. 5). The absolute value of the difference between
estimated distance and actual distance does not show the trend as clearly, because variations
about zero have the same effect on this measure as a consistent bias (a consistent overestimate or
underestimate).

An analysis of variance (ANOVA) can be applied to the results, ignoring one condition.
One may question if performance changed from the pretest condition to the first posttest
condition. (One group of subjects received two posttest conditions; we set aside their second
posttest for the purposes of this single analysis.) There are various ways to ask this question,
corresponding to different dependent measures. Let us consider the log ratio of the estimated and
actual distances. This measure is not susceptible to the effects of skew in observations, as are the
signed difference of the estimated and actual distances, or the absolute value of that difference.
One observer failed to make one judgment: A mean value for the condition was substituted for
this missing datum. Then we can perform a three-way repeated measures ANOVA on the data
for all twelve observers, to ask three main questions: (1) Is there a difference between pretest
and first posttest conditions on the dependent measure?, (2) Is there a difference between
estimates taken at a standing position and estimates taken at an elevated position?, and (3) Is
there a difference between distances from the observer to a target and distances between two
targets, that is, between egocentric and exocentric distances? Call the factors that correspond to
these questions Test, Position, and Distance Type, respectively. Of course, the possibilities of
interaction between these factors are also evaluated in the ANOVA. (The summary of this
ANOVA is listed as Table 2.) The statistics associated with two of the main effects are
significant in this analysis: the effect of Test F(1,11) = 10.21, p < .01 and the effect of Distance
Type F(1,11) = 55.35, p< .01. None of the other effects is significant. This indicates that scores
changed between pretest and posttest, and scores were different for egocentric distances than for
exocentric distances. What this leaves unsaid is whether these changes are improvements. An
improvement occurs when the observer’s estimate and the actual distance become similar, that is,



20
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pretest
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Figure 5. Effect of Feedback on Distance Estimates

Training with feedback improves distance estimates. Mean errors are plotted by successive trials in the experiment
(.e., pretest, first training trial, second training trial, immediate posttest, and posttest at one week). The signed
difference of distance estimates from ground distance is plotted, and the ratio of distance estimates to ground distance is
plotted separately. Standard error bars are shown. Means for the first three trials (pretest, first training trial, second
training trial) are based on 240 observations, while means for the latter two trials (posttests) are based on 160
observations. The dashed line in each graph indicates ideal performance on the measure.

1



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4. TITLE AND SUBTITLE 5. FUNDING NUMBERS

. 7 C_ - F41625-95-C-5011
Distance Estimation with Night Vision Goggles: A Direct Feedback Training Method | pe - 62202F

6. AUTHOR(S) m : Be Be

Keith K. Niall Elizabeth L. Martin WU - 06, 06

Jack D. Reising Marcus H. Gregory

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) REA OME C NIZATION
9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSORING MONTTORING

Armstrong Laboratory
Human Resources Directorate
Aircrew Training Research Division AL/HR-TR-1996-0148
6001 South Power Road, Building 558
Mesa AZ 85206-0904

11. SUPPLEMENTARY NOTES.

Armstrong Laboratory Principal Investigator: Dr Elizabeth L. Martin (602) 988-6561

12a. DISTRIBUTION/AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE

Approved for public release; distribution is unlimited.

13. ABSTRACT (Maximum 200 words)

An experimental demonstration was made of the efficacy of immediate feedback in improving observers’ estimates of distance
where those estimates were made outdoors at night while wearing night vision goggles (NVGs). Initially, observers made
unguided estimates of distances between marked positions in an open field. Those distances ranged from 25 ft to 210 ft.
Later, the same observers made more estimates. After each, they were told the measured distance between the positions.
During this training, the observers’ eye height from the ground plane was either at a standing position or at an elevated position
(12 ft from the ground). After the training--either immediately after, or after a week, or at both times--observers made
unguided estimates of distance again. These estimates of ground distance made with the NVGs were significantly improved
from the first unguided estimates; average improvement for the group of observers persisted for at least one week after
training. Direct feedback training appears to be more effective at improving performance at distance estimation (in terms of
both precision and error variability) than the training assessed in previous experiments where no verbal feedback was given.

14. SUBJECT TERMS ; ; oo. 15. NUMBER OF PAGES
Distance perception; Feedback; Knowledge of results; Linear perspective; Night vision 35

goggles; NVGs; Training; Optical aids 16. PRICE CODE

17. SECURITY CLASSIFICATION | 18. SECURITY CLASSIFICATION | 19. SECURITY CLASSIFICATION
OF REPORT OF THIS PAGE OF ABSTRACT 20. LIMITATION ABSTRACT
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Prescribed by ANSI Std Z-39-18



© Observer three

© Observer six

© Observer nine

= Observer twelve

Moving average
{estimated distance / actual distance)

02

20 40 60 80 100
Number of judgments

Figure 8. Concluded

A 21-point moving average is plotted for the second through fourth trials of the experiment (the first training:
judgments 21 to 40; second training: judgments 41 to 60, first posttest: judgments 61 to 80; and second posttest:
judgments 81 to 100) by number of judgments made by each observer. The moving average is computed on the ratio
of estimated distance to actual distance. Individual results are plotted; not all observers took part in all the posttest
conditions.

condition of the experiment, estimated distances are not well predicted either by visual angle or
the tangent of visual angle.

Visual angle is computed by considering the idealized eye position of the observer, and
the two end locations of the distance in question. The eye height of the observer is considered to
be 5 ft in the standing condition, and 12 ft 7 in. in the elevated condition. Three direction cosines
from the eye position of the observer are computed to each of the two locations. (Direction
cosines can be considered as the projected lengths of a given line length on the x, y, and z axes of
a coordinate system. Three direction cosines correspond to each length.) If the eye position at
the origin of coordinates is designated by O, and the ends of the distance in question are
designated P and Q, then we wish to find the angle between lines OP and OQ. If OP has
direction-cosines cos «, cos B, and cos y, and OQ has direction-cosines cos a‘, cos B‘, and cos y‘,
then the angle @ that OP makes with O0 is given by:

cos ® = cosa cos a + cos B cos BS + cos y cos y‘

20



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The Office of Public Affairs has reviewed this paper, and it is releasable
to the National Technical Information Service, where it will be available to the
general public, including foreign nationals.

This paper has been reviewed and is approved for publication.

ELIZABETH L. MARTIN DEE H. ANDREWS
Project Scientist Technical Director

LYNN A. CARROLL, Colonel, USAF
Chief, Aircrew Training Research Division

Please notify AL/HRPP, 7909 Lindbergh Drive, Brooks AFB, TX 78235-5352, if your .
address changes, or if you no longer want to receive our technical reports. You may
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Reising, J. D., & Martin, E. L. (1994). Distance estimation training with night vision goggles: A
preliminary study. (AL/HR-TR-1994-0090, AD A284 900). Mesa, Arizona: Armstrong
Laboratory, Human Resources Directorate, Aircrew Training Research Division.

Reising, J. D., & Martin, E. L. (1995). Distance estimation training with night vision goggles under

low illumination. (AL/HR-TR-1994-0138, AD A291 338). Mesa, Arizona: Armstrong
Laboratory, Human Resources Directorate, Aircrew Training Research Division.

28



Table 7. Partial Correlation of Distance and Visual Angle with Responses

Partial correlations can be taken to gauge the relative contributions of actual distance and visual angle to the prediction
of distance estimates. These correlations are tabled for the training trials and retention trials of the experiment.
Separate correlations are drawn for distances from the observer to a target (“egocentric distances”) and distances
between targets (“exocentric distances”). The correlation of actual distance and estimated distance is high and
significant, even when the effect of visual angle is taken into account. In contrast, the correlation between visual angle
and estimated distance is nonsignificant and approaches zero when the effect of actual distance is taken into account.
The data of the experiment are better explained by saying that observers base their estimates of distance on actual
distance, and not on the magnitude of visual angle. (This seems a common-sense proposition: that when asked and able
to judge distance, observers will judge distance, and not some other thing.)

First variable: actual distance (1)

Second variable: estimated distance (2)

Third variable: tangent of angle (3)

Condition Trials R123 R23.1 n
Egocentric 2,3 0.85 -0.05 192
Egocentric 4,5 0.70 -0.10 128
Exocentric 2,3 0.85 0.00 287
Exocentric 4,5 0.80 0.04 192

A related question concerns the special status of so-called “egocentric” distances. These
distances radial to the observer are distinguished by their geometry, as may be seen by the
relation of distance to subtense of visual angle in the experiment (plotted in Fig. 9). Egocentric
distances are distances most severely foreshortened (their angular subtense is nearest 90 deg,
from the observer’s feet to the horizon). Elevation of the observer does change this
foreshortening somewhat (as can be seen from the parallel curves of black dots in the diagram),
but the variation in angular subtense is not as great as that among the exocentric distances. The
effect of foreshortening follows the cosine of this angular subtense. (Remember that the
egocentric distances are close to being seen end-on, that is, close to not being seen at all.) It is
the property of geometric foreshortening that distinguishes these stimuli; that is, they are
distinguished by their geometric or optical properties, and not as the result of an automatic but
unconscious computational process. Foreshortening is not a cue to distance, or an aid to the
estimation of distance; it is a positive impediment to the estimation of distance, that is a fixed

23



Procedure

Pretest. This part of the procedure assessed the accuracy of observers’ distance estimates
in the absence of formal training; the data from this portion of the experiment serve as a baseline
for assessing the impact of the training procedure. The observers first adjusted the NVGs using
the infinity focus system. They were then either positioned on the ground (immediately under the
stand) or elevated on top of the stand. Four of the eight targets were used for distance judgments at
one time. All targets were readily distinguished (under NVG viewing conditions) by labels on
which large black numbers were printed. Observation position (ground or elevated) was
manipulated.

The observers were required to judge all distances between four targets (six distances) as
well as the ground distances of each of the four targets to their own position (four distances). The
targets were configured in the field in a pre-defined random arrangement, among 64 possible
positions. The observer made ten judgments of the distances of these targets from one another,
that is, of a group of four targets (of the eight present in the field). The observer also made
judgments of the distances of each of these targets from her or his own position (cf. Figs. 3 and
4). For example, if the targets are {1,2,3,4} and the observer’s position is {0}, then the pairs that
define the distances to be judged are: {1,2; 1,3; 1,4; 1,0; 2,3; 2,4; 2,0; 3,4; 3,0; 4,0}. The
observer made these judgments from one of two positions, either STANDING at the edge of the
field, or ELEVATED on a stand, so that the eye height of the observer was raised 7 ft 7 in. The
starting position of the observers was counterbalanced. The order in which these distances were
judged was randomized, and dictated by the experimenter. After judging ten distances, subjects
were repositioned (to the ground or else elevated on the platform, depending upon their starting
location), and asked to judge another ten distances on the second four targets. The observers’
verbal estimates of distance were recorded by the experimenter. Observers were not given a
specific time limit in which to make their estimates.

Training. After pretesting, observers were given training. Half the observers were trained
on the ground only and the other half were trained on the stand only. Two target sets were used for
training. The first target set was the same eight targets used during the pretest. Observers were
asked to estimate twenty distances, and the experimenter provided verbal feedback. The actual
distance was provided verbally by way of feedback immediately after each estimate was made.
After the first target set (20 distances) was estimated and corrected, the target positions were
reconfigured, and 20 more distances were estimated and corrected. This training lasted for
approximately 15 to 20 minutes.

Posttest. After training, a posttest was administered. A new target set was used, and the
posttest procedure was the same as the pretest--no feedback was administered. Each observer was
assigned to one of three groups, and each group included four observers. The groups differed in
the posttest conditions. Posttests occurred either immediately after the second training period, or
one week after training. One group received the immediate posttest only, another group received
only the posttest after one week, and a third group received both the immediate and one-week
posttest.



Table 1. Accuracy Over Trials, as Assessed by Three Dependent Measures

Accuracy of performance in the experiment can be assessed in several ways. Here, mean
accuracy across trials is tabled in terms of the signed difference of estimated distance minus
actual distance, the ratio of estimated distance to actual distance, and the absolute value of the
difference between estimated distance versus actual distance. Generally, performance improves
between the first trial and the second, and observers make precise estimates of distance in Trials
2 through 5 on average. The third dependent variable--the absolute value of the difference
between estimated distance and actual distance--shows the trend less clearly, because variations
of the measure about zero have the same effect on the measure as a constant bias, ie., asa

consistent overestimate or underestimate.

Dependent measure (ft)

Trial Estimated - Actual s.e. n
1 -19 3 240
2 -2 2 239
3 -1 2 240
4 -1 2 160
5 -1 2 160
Trial Estimated / Actual S.e. n
1 0.79 0.02 240
2 1.00 0.02 239
3 1.00 0.02 240
4 1.01 0.02 160
5 1.02 0.03 160
Trial Abs (Estimated - Actual. S.e. n
1 39 2 240
2 21 1 239
3 18 1 240
4 23 1 160
5 26 2 160
10